Priority -Oriented S-Box : A Priority Based Optimization of Encryption for Embedded System Wireless Sensor Nodes

Cryptographic substitution boxes (S-boxes) are central to the security of symmetric ciphers especially for light weight embedded system sensor nodes. However, their design remains a challenging multi-objective optimization task due to conflicting requirements such as nonlinearity, differential uniformity, avalanche effect, and bit independence. Existing weighted-sum or Pareto-based approaches often fail to enforce strict prioritization when specific cryptographic properties are more critical than others. This work introduces a novel lexicographic optimization framework based on Self-Adaptive Differential Evolution (SADE) with priority relaxation. The method enforces a hierarchy of objectives, ensuring that high-priority metrics are satisfied before optimizing secondary ones, while introducing relaxation once thresholds are achieved to avoid overfitting a single property. A rank-based permutation encoding guarantees bijective 8-bit S-box mappings without repair mechanisms. Experimental results demonstrate that the framework consistently produces S-boxes with strong cryptographic properties, including nonlinearity above 107 and differential uniformity as low as 8, comparable to state-of-the-art evolutionary and chaotic optimization methods. The proposed scheme is particularly suited for IoT and lightweight encryption systems where application-specific prioritization of cryptographic strength is essential. The acquired configuration was evaluated on a ensilica Xtensa L106 embeeded system with selectable ’priority’ configurations.